Relatório de pesquisa 12/08
Fractional Term Structure Models: No-Arbitrage and Consistency, Alberto Ohashi,
submitted June 10.
Abstract
In this work we introduce Heath-Jarrow-Morton (HJM) interest
rate models driven by fractional Brownian motions. By using support
arguments we prove that the resulting model is arbitrage-free under
proportional transaction costs in the same spirit of Guasoni et al [20,
21, 22]. In particular, we obtain a drift condition which is similar in
nature to the classical HJM no-arbitrage drift restriction. The second
part of this paper deals with consistency problems related to the
fractional HJM dynamics. We give a fairly complete characterization of
finitedimensional invariant manifolds for HJM models with fractional
Brownian motion by means of Nagumo-type conditions. As an application,
we investigate consistency of Nelson-Siegel family with respect to
Ho-Lee and Hull-White models. It turns out that similar to the Brownian
case such family does not go well with the fractional HJM dynamics with
deterministic volatility. In fact, there is no nontrivial fractional
interest rate model consistent with the Nelson-Siegel family.
Mathematics Subject Classifications
(2000):
Keywords: Fractional Brownian motion. Interest rate models. Stochastic PDEs. Invariant manifolds. Nelson-Siegel family
Copy
of the file:
rp12-08.pdf
(PDF)
rp12-08.pdf.gz (gzipped PDF)
June 10, 2008
Volta ao
indíce de Relatórios de Pesquisa